About the Average Atomic Mass Calculator
This average atomic mass calculator turns a list of isotopes into the single atomic weight you see on the periodic table. Enter the mass of each isotope in unified atomic mass units (u, also written amu or Da) and its natural abundance as a percentage, and it returns the abundance-weighted mean along with how much each isotope contributes.
It is aimed at chemistry students working isotope problems, teachers building examples, and anyone reading mass-spectrometry data who wants to check that relative peak heights reproduce a known atomic weight. You can model up to five isotopes, which covers most textbook problems and many elements; a few, such as tin (ten stable isotopes) and xenon (nine), have more.
Abundances should add up to 100%. If they do not — for example when you type rounded values or peak intensities instead of percentages — the calculator divides by their actual total, so relative abundances work too, and it tells you what the total was.
With the default inputs, the average atomic mass is 35.4529 u. Change any value above to recalculate instantly.
How to use the average atomic mass calculator
- 1Choose how many isotopes the element has.
- 2Enter each isotope’s exact mass in u (not its mass number, if you have the precise value).
- 3Enter each natural abundance as a percentage.
- 4Read the weighted average atomic mass and check the abundance total.
Formula and method
The average atomic mass is a weighted mean: each isotope’s mass is multiplied by its fractional abundance and the products are added. With percentages, fractional abundance is the percent divided by 100 — or, more generally, divided by the sum of all abundances entered, which is what this tool does so that relative intensities from a mass spectrum also work.
Because the weights are fractions of atoms, the result always lies between the lightest and heaviest isotope mass and is pulled toward the most abundant isotope. The same number in grams per mole is the element’s molar mass.
- mᵢ
- Mass of isotope i, in u (amu, Da)
- fᵢ
- Fractional abundance of isotope i (0–1)
- Σ
- Sum over all isotopes entered
Worked examples
Chlorine (Cl-35 and Cl-37)
Chlorine is 75.76% Cl-35 (34.96885 u) and 24.24% Cl-37 (36.96590 u). 34.96885 × 0.7576 + 36.96590 × 0.2424 = 35.453 u, matching the periodic-table value of 35.45.
Magnesium with three isotopes
Weighting 23.98504 u by 78.99%, 24.98584 u by 10.00% and 25.98259 u by 11.01% gives 18.9458 + 2.4986 + 2.8607 = 24.305 u.
Copper from rounded abundances
The rounded abundances add to 100.1%, so each is divided by 100.1: (62.9296 × 69.2 + 64.9278 × 30.9) ÷ 100.1 ≈ 63.547 u, essentially copper’s standard atomic weight of 63.546.
Frequently asked questions
How do you calculate average atomic mass?+
Multiply each isotope’s mass by its abundance written as a decimal (75.76% becomes 0.7576) and add the results. For chlorine that is 34.969 × 0.7576 + 36.966 × 0.2424 ≈ 35.45 u.
Why is average atomic mass not a whole number?+
It is a weighted mean of several isotopes with different masses, and each isotope’s exact mass also differs slightly from its mass number because of nuclear binding energy. Only single-isotope elements come close to whole numbers.
How do I find an unknown isotope abundance?+
For two isotopes, set the abundances to x and 1 − x and solve average = m₁x + m₂(1 − x), so x = (m₂ − average) ÷ (m₂ − m₁). You can then check the answer here.
Is atomic mass the same as mass number?+
No. Mass number is the whole-number count of protons plus neutrons in one isotope. Atomic mass is the measured mass of that isotope in u, and the average atomic mass combines all isotopes by abundance.
What units does average atomic mass use?+
Unified atomic mass units (u), also called daltons (Da) or amu. One mole of the element has a mass in grams equal to the same number, so 35.45 u corresponds to 35.45 g/mol.